CIRM Povo (Trento) 1-5 December 2014

A complex transition: German general and review journals to specialized journals in the early 19th century

Tom ARCHIBALD (Simon Fraser University, Vancouver, Canada)

The general and review journals, very numerous in the later years of the 19thcentury, give evidence of much general interest in mathematics. The passage to research journals, notably that of Crelle, attempted to retain the audience by a variety of strategies. In this paper we examine the characteristics of mathematics in the general journals, the volumes that are reviewed, and the strategies of Crelle and others to interest broader publics in more advanced and difficult subjects.

Il Giornale di Matematica di Battaglini e le relazioni internazionali

Maria Rosaria ENEA (Dip. Matematica, Univ. Basilicata)

Il Giornale di Matematiche was the first mathematics’ journal founded in an Italian university after the Unification in 1860. It was born on the initiative of a professors’ group from the University of Naples, to provide Italian universities with a journal that could make the developments of European mathematics known, especially to young people. According to the promoters of the initiative, this scientific journal had to lead young scholars to the difficult path of mathematical research.

Veronica GAVAGNA (Dip. Matematica Univ. Salerno)

Even though Leonardo Pisano’s Liber Abaci was written in Latin, the Italian tradition of practical mathematics and algebra – started from the beginning of 13th century and developed till the 16th century – has been mostly a vernacular and local tradition. The invention of the movable type printing technology did not change this aspect: the best appreciated and spread abacus treatises, that is Pacioli’Summa, Borghi’s Libro de abacho – to mention only the most famous – were still in vernacular and mirrored an everyday life geographically limited. Girolamo Cardano’s Practica arithmetice (1539) represented a breakpoint in this trend. Cardano decided to write in Latin his first mathematical work, a kind of abacus treatise, to enlarge his public to the intellectual environments and to make his Practica one of the main means for spreading the practical mathematics throughout Europe. It was not an easy operation, as it presented – just to take an example – the difficulty of translating some particular expression of the abacus vulgar lexicon in latin terms. Nevertheless it was a successfull operation: Viète, Stiffel, Nunez and others often mentioned Cardano’s Practica. But Cardano’s project was much more ambitious. His following goal was to publish an encyclopedia of practical arithmetics in fifteen volumes, called Opus arithmetice perfectum. He was not able to complete his project, but we have some volumes (Ars magna, Opus novum de proportionibus) and fragments still extant that shed a light on this work, aimed to go beyond the abacus environments so to give a transnational dimension to the practical arithmetics. This encyclopedia, inspired to the architecture of Euclid’s Elements, was to be a reference point in the whole mathematical community. This was the reason why, for example, Cardano adopted a completely different approach in respect with the Practica, abandoning the terminology of the abacus for a lexis more representative of the purity of Latin. My talk is focused in describing the features and the fortune of Cardano’s editorial project, interpreted as an attempt to transform a mainly local phenomenon into a tool shared by a wider community to stimulate the development of mathematics. Bibliography G. CARDANO, De libris propriis. The editions of 1544, 1550, 1557, 1562 with supplementary material, edited by I. MACLEAN, Milano, Angeli 2004. V. GAVAGNA, Medieval Heritage and New Perspectives in Cardano’s Practica arithmetice, Bollettino di Storia delle Scienze Matematiche, (30) 2010, pp. 61-8. V. GAVAGNA, L’Ars magna arithmeticae nel corpus matematico di Cardano, in S.Rommevaux, M.Spiesser e M.Massa Estève (eds.), Pluralité de l’algèbre à la Renaissance, Paris, H.Champion Éd., 2012, pp. 237-268. M. TAMBORINI, Per una storia dell’Opus Arithmeticae Perfectum, in M.L. BALDI, G. CANZIANI (eds.) Cardano e la tradizione dei saperi, Milano, F. Angeli 2003, pp.157-189.

The first thirty years of the Italian Mathematical Union, through its Bollettino: between nationalism and internationalization.

Livia GIACARDI (Dip. Matematica Univ. Torino)

The talk will present a first attempt to reconstruct the history of the first thirty years of the Unione Matematica Italiana (UMI), situating it into the scientific, political and international context. The timeframe spans from 1922, the year of its founding, to 1952, when the IMU was refounded in Rome and Enrico Bompiani, president of the UMI starting in the year, became secretary. The principal sources of the research are the “Bollettino della Unione Matematica Italiana”, the unpublished documents and letters (Pincherle, Bortolotti, Volterra, Castelnuovo, Mussolini, Picard, Koenig, Mittag-Leffler, Courant, and others) conserved in the Archives of the UMI and of the Accademia dei Lincei as well as archives in other countries, the proceedings of the national UMI congresses and those of the International Congresses of Mathematicians (ICMs). The aspects to be explored are:

● the difficulties of the beginnings of the UMI, related to problems of national politics (the birth of Fascism) and global politics (the after-effects of World War I), and to the relationships with other associations of mathematicians already in existence (Circolo Matematico di Palermo, Mathesis);

● the difficult path towards internationality, whose most important step was the organisation of the 1928 ICM in Bologna, during which Pincherle played the dual role of president of the UMI as well as of the IMU. Pincherle, extending the invitation to all nations without distinction, and thus welcoming also the mathematicians of the Central Powers, including Germany, succeeded in breaking down the “political barriers”, thus achieving that internationality of science which has been compromised in 1920 during the ICM in Strasbourg by the exclusion of the scientists of the Central Powers from the international cooperation. Pincherle’s negotiations are well documented in the rich correspondence held in the UMI Archive.

● The role played by relationships with Fascism, especially following the emanation of the racial laws, which seem to have negatively influenced the opportunities for international relations that appear to have increased after 1948;

● The broadening of the range of action of the UMI, which, starting in 1939, began to occupy itself with questions pertaining to mathematics teaching. References Giacardi, L. 2008 Timeline in The first century of the International Commission on Mathematical Instruction (1908-2008): http://www.icmihistory.unito.it/timeline.php Guerraggio, A., Nastasi, P. 2005, Matematica in camicia nera, Mondadori, Milano, 2005. Lehto, O. 1998, Mathematics Without Borders. A History of the International Mathematical Union, Springer, New York. Pucci, C. 1986, L’Unione Matematica Italiana dal 1922 al 1944: documenti e riflessioni, in Symposia mathematica (ed. INDAM), vol. 27, pp. 187-212.

The international partnerships on mathematical instruction at the age of Totalitarianism

Erika LUCIANO (Dip. Matematica Univ. Torino)

As is well known, an articulated process of ideological indoctrination, known as the fascistization of school and research, was put into place in Italy during the dictatorship (1922-1945). This process went hand in hand with a focused strategy of closure and boycotting of international scientific trends and experiences, known as the policy of cultural autarchy. In particular, after 1936 scientific exchanges of teachers and students were systematically discouraged; famous scholars such as G. Fubini and G. Colonnetti, were refused passports to attend international congresses or to teach abroad as visiting professors, and even foreign books, journals and teaching materials were subjected to severe controls. On the contrary, favoured intellectuals of the regime, such as F. Severi, E. Bompiani, L. Fantappiè, were often invited as lecturers in France, German, Japan, Brazil, Scandinavia, and took the opportunity to celebrate the superiority of Latin genius and the success of the cultural lines promoted by the fascist dictatorship. Analysing the correspondences and the publications of this period, and thanks to sources preserved in some Italian archives (the Historical Archives of the Turin University and Polytechnic, the archive of FESE [Fond Européen de Secours aux Etudiants], the archive of Del.As.Em, [Delegazione per l’assistenza agli emigranti ebrei], the network of correspondences among V. Volterra, G. Castelnuovo and F. Enriques, …), in this talk we will illustrate: – the repercussions of cultural autarchy on the evolution of Italian mathematics; – the strategies adopted by some scholars (G. Castelnuovo, F. Enriques, V. Volterra, A. Terracini, F.G. Tricomi, E. Persico, F. Severi, E. Bompiani, L. Fantappié, …), in order to mitigate the effects of this forced scientific isolation and – the tension – under a totalitarian regime – between the physical control over individuals and objects, and the free supranational circulation of scientific knowledge and ideas. References GOODSTEIN J., BABBITT D., A fresh look at Francesco Severi, Notices of the AMS, 59, n. 8, pp. 1064-1075. GUERRAGGIO A., NASTASI P. (eds.), Italian mathematics between the two world wars, Basel, Birkhäuser, 2005. LUCIANO E., Matematica e ideologia. Momenti di storia dell’insegnamento nel ventennio fascista, Atti dell’Istituto Veneto di Scienze, Lettere ed Arti, Classe di scienze fisiche, matematiche e naturali, 172, 2013-14, pp. 235-276. NASTASI P. TAZZIOLI R., I matematici italiani e l’internazionalismo scientifico (1914-1924), La Matematica nella Società e nella Cultura, Rivista dell’Unione Matematica Italiana, s. 1, VI, 2013, pp. 355-405. PARSHALL K.H., RICE A.C. (eds.), Mathematics Unbound: the Evolution of an International Mathematical Research Community 1800-1945, Providence. Rhode Island, AMS, 2002. SIEGMUND-SCHULTZE R., Rockefeller and the Internationalization of Mathematics between the Two World Wars, Basel, Birkhäuser, 2001. SIGNORI E., Una «peregrinatio academica» in età contemporanea. Gli studenti ebrei stranieri nelle università italiane tra le due guerre, Annali di storia delle università italiane, 4, 2000, pp. 139-162. VOIGT K., Il rifugio precario. Gli esuli in Italia dal 1933 al 1945, Firenze, La Nuova Italia, 1989.

Iolanda NAGLIATI (Univ. Ferrara)

The University of Pisa has a long tradition in the field of scientific journals, starting from the last decades in XVII century, that set it in a peculiar position between the academic institutions of the time. The first period is under the name of Giornale dei letterati, published from 1771 to 1839, with some changes in the title and long interruptions, followed by some series of the Giornale Toscano and collected papers concerning scientific topics, then from 1846 by the Annali delle università toscane, until 1925, and finally from 1871 by the Annali della Scuola Normale. The Giornale took place as the expression of the board of professors, directed by the superintendent Angelo Fabroni. This close relationship with the university was an advantage for the magazine, kept out from the control of religious authorities, but at the same time a limit, with regard to the level of non-uniform scientific contributions of teachers. Fabroni had a large network of relationship with both individuals (d’Alembert, Condorcet, J.D. Cassini, Lalande, Waring, Priestley) and institutions in Europe (Royal Society, Académie des Sciences). The journal become one of the most influential literary review of the time, and also from the mathematical point of view it has interesting elements, most of all for the presence of excerpts from the main foreign journals and reviews of works recently published. The attention paid to the developments of sciences in the European framework was a constant of the Giornale dei letterati, that ended its life after the first Congress of Italian scientists, held in Pisa in 1839. A different purpose inspired the Annali delle università toscane, whose aim was to give to the professors a place to publish not only research articles, but also lessons, critical editions, treatises, etc., without external contributions. Finally in 1871 the most famous mathematician working in Pisa, Enrico Betti, edited the Annali della Scuola Normale, containing the best thesis of the students; this journal played a significant role in the development of the international dimension of the Italian research, due to the large reached number of interchanges between universities. Bibliography: – Capecchi Silvia (cur), Giornali del Settecento fra Granducato e Legazioni (atti del convegno di studi, Firenze, 17-19 maggio 2006), Roma, Edizioni di storia e letteratura, 2008 – Nagliati Iolanda, La matematica nei giornali toscani dell’Ottocento, in: Pepe L. (a cura di), Europa matematica e Risorgimento italiano, Bologna, Clueb, 2012, p. 199-208 – Pepe Luigi, Matematica e matematici nella Scuola Normale di Pisa 1862-1918, in Annali di storia delle università italiane, 15, 2011, p.67-80 – Tomassini Giuseppe, Gli « Annali » della classe di Scienze, in Annali di storia delle università italiane, 15, 2011, p. 213-220.

The diffusion in Italy of S. Lie’s theory on continuous transformation groups. The role of C. Segre and his followers

Maria Anna RASPANTI (Dip. Matematica Univ. Torino)

The aim of my research is to analyze the influence of the diffusion of Sophus Lie’s (1842-1899) theory of continuous transformation groups on the development of Italian mathematics, in particular in the field of algebraic geometry, thanks to Corrado Segre’s (1863-1924) scientific, didactic and promoting activity. Segre’s interest in Lie’s groups theory and in its applications (especially to geometry as a consequence of Felix Klein’s Erlangen Program) comes out from some of his writings (stored in the mathematics library, entitled to Giuseppe Peano, of the University of Turin), among which one can find the Quaderno 11, relating to his Superior Geometry course held in academic year 1897-98, entitled Lezioni sui gruppi continui di trasformazioni. Among the students who attended the course there were Mr. and Mrs. William and Grace Young, whose notes have been used for a comparison of the contents (Archives – University of Liverpool). Italian geometers (in particular, those close to Corrado Segre’s school), played an important role in the connection between Lie’s groups theory and geometry; a proof of this can be found in some of such geometers’ – among which Federigo Enriques (1871-1946) and Gino Fano (1871-1952) – writings.